primes

I'm new to Haskell, and I'm trying a bit: isPrime :: Integer->Bool isPrime x = ([] == [y | y<-[2..floor (sqrt x)], mod x y == 0]) I have a few questions. Why when I try to load the .hs, WinHugs say: Instances of (Floating Integer, RealFrac Integer) required for definition of isPrime ? When the interpreter finds one element in the right set, it immediately stops or it computes all the set? I think you know what I mean. Sorry about my english. 1) The problem is that sqrt has the type (Floating a) => a -> a , but you try to use an Integer as argument. So you have to convert your Integer first to

I know the Miller–Rabin primality test is probabilistic. However I want to use it for a programming task that leaves no room for error. Can we assume that it is correct with very high probability if the input numbers are 64-bit integers (i.e. long long in C)? Miller–Rabin is indeed probabilistic, but you can trade accuracy for computation time arbitrarily. If the number you test is prime, it will always give the correct answer. The problematic case is when a number is composite, but is reported to be prime. We can bound the probability of this error using the formula on Wikipedia : If you

The question is to find the 1000th prime number. I wrote the following python code for this. The problem is, I get the right answer for the 10th , 20th prime but after that each increment of 10 leaves me one off the mark. I can't catch the bug here :( count=1 #to keep count of prime numbers primes=() #tuple to hold primes candidate=3 #variable to test for primes while count<20: for x in range(2,candidate): if candidate%x==0: candidate=candidate+2 else : pass primes=primes+(candidate,) candidate=candidate+2 count=count+1 print primes print "20th prime is ", primes[-1] In case you're wondering,

Is there a straightforward way to extracting the exponent from a power of 2 using bitwise operations only? EDIT: Although the question was originally about bitwise operations, the thread is a good read also if you are wondering "What's the fastest way to find X given Y = 2 X in Python ?"** I am currently trying to optimize a routine ( Rabin-Miller primality test ) that reduces an even number N in the forms 2**s * d . I can get the 2**s part by: two_power_s = N & -N but I can't find a way to extract just " s " with a bitwise operation. Workarounds I am currently testing without too much

This question follows on the answer given by Jon Skeet on the question: " What is the best algorithm for an overridden System.Object.GetHashCode? ". To calculate the hash code the following algorithm is used: public override int GetHashCode() { unchecked // Overflow is fine, just wrap { int hash = 17; // Suitable nullity checks etc, of course :) hash = hash * 23 + field1.GetHashCode(); hash = hash * 23 + field2.GetHashCode(); hash = hash * 23 + field3.GetHashCode(); return hash; } } I don't understand why the numbers 17 and 23 are chosen. Why don't we pick 3 and 5? That are prime numbers as

How do I quickly generate a random prime number, that is for sure 1024 bit long? Generate 1024 random bits. Use a random source that is strong enough for your intended purpose. Set the highest and lowest bits to 1. This makes sure there are no leading zeros (the prime candidate is big enough) and it is not an even number (definitely not prime). Test for primality . If it's not a prime, go back to 1. Alternatively, use a library function that generates primes for you. Use a library function, such as OpenSSL. There's no need to write this yourself. Example: http://ardoino.com/7-maths-openssl